Abstract
Strongly correlated materials include hosts of some of the most exciting topics in condensed matter physics, such as conventional and high-Tc superconductors, multiferroics, Mott insulators, spin/charge-density-wave materials, and topological insulators. The electron-electron correlation plays a critical role in these systems, and in many case the correlation is a result of two competing order parameters. It is therefore important to understand the interplay between the competing orders. One approach is to study the domain topology, since the competing between different long-range orders will have an impact on the spatial distribution of domains associated with each orders. The most direct experimental ways of studying domain topology are surface probes such as scanning/tunneling electron microscopes and second harmonic generation, as well as bulk probes such as focused ion beam microscope. On the other hand, neutron/X-ray scatterings, and magnetic susceptibility, transport and heat capacity measurements can give indirect information on domain topology. Both the direct and indirect data can be compared with Monte Carlo simulations to give information on the competing orders.
The electric field effect on the magnetic order in LuMnO3 and the Fe vacancy order in KxFe{2-y}Se2 are discussed in this thesis. In both projects, neutron and X-ray scattering experiments were performed to investigate the microscopic details of the system including nuclear and magnetic structures, phase volume fractions, and spin wave excitations. The information obtained from scattering was compared with simulation results using Monte Carlo method. Although the Monte Carlo models used in both projects were constructed based on lattice symmetries without microscopic details, the simulation results were still able to characterize the key features in the experiments. In LuMnO3 ferroelectric domain walls are coupled with the magnetic domain walls, and the external electric field has an effect on the magnetic order through the change of the domain wall distribution. In KxFe{2-y}Se2, phase separation exists in the form of coexisting domains of the vacancy-ordered and vacancy-free phases with disordered vacancies on the domain boundaries. Post-annealing and quenching increases the volume fraction of the domain boundary as well as the Meissner shielding fraction, indicating that the vacancy disorder on these boundaries gives rise to superconductivity. In both works, the domain topology is shown to be related to the competing orders, and can be associated with novel properties such as superconductivity and the coupling between multiferroic orders.
